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This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…

We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Mat\'ern prior as continuous-parameter random…

The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data…

There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing…

In this big data era, the use of large dataset in conjunction with machine learning (ML) has been increasingly popular in both industry and academia. In recent times, the field of materials science is also undergoing a big data revolution,…

Regression methods dominate the practice of biostatistical analysis, but biostatistical training emphasises the details of regression models and methods ahead of the purposes for which such modelling might be useful. More broadly,…

The need for new methods to deal with big data is a common theme in most scientific fields, although its definition tends to vary with the context. Statistical ideas are an essential part of this, and as a partial response, a thematic…

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…

Deep learning based localization and mapping has recently attracted significant attention. Instead of creating hand-designed algorithms through exploitation of physical models or geometric theories, deep learning based solutions provide an…

We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks,…

Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…

This paper describes and discusses Bayesian Neural Network (BNN). The paper showcases a few different applications of them for classification and regression problems. BNNs are comprised of a Probabilistic Model and a Neural Network. The…

Simulation has become a standard tool in statistics because it may be the only tool available for analysing some classes of probabilistic models. We review in this paper simulation tools that have been specifically derived to address…

The Matern family of covariance functions is currently the most commonly used for the analysis of geostatistical data due to its ability to describe different smoothness behaviors. Yet, in many applications the smoothness parameter is set…

Geological maps are an extremely valuable source of information for the Earth sciences. They provide insights into mineral exploration, vulnerability to natural hazards, and many other applications. These maps are created using numerical or…

Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…

Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial…

Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…

A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…

There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…